Event Tree Construction
An event tree is a visual representation of the events that may occur in a system. You can use event trees to analyze both continually operating and standby systems. In either case, the event tree consists of branches that represent the success or failure of the components in the system.
For example, you can construct a simple event tree to analyze the possible outcomes for a fire alarm system. This system has two components designed to handle an occurrence of a fire:
• A sprinkler system to contain the fire.
• An automated call system to notify the fire department.
If the automated call system fails, the fire department is not notified automatically; however, the sprinkler system should contain the fire. If both the automated call system and the sprinkler system fail, the fire alarm system will be destroyed.
You can insert additional columns (events) in the event tree. For example, you might insert a column for the detection sensor that turns on the sprinkler system or the event that the fire department does not receive the automated call. As more events are taken into consideration, an event tree can grow significantly.
It is best to reduce an event tree to the fewest number of events that result in an particular outcome. For example, if power to the system is lost, no need to evaluate the success or failure of various system components exist because the entire system will be inoperable. Reducing an event tree to consider only significant events makes it easier to understand the event tree as well as reduces the time it takes to calculate results.
Once the event tree is constructed, the frequency or probability of each consequence (outcome) can be computed. In the example above, the calculations are done to determine the likelihood or frequency of the system surviving (consequence 1), partial damage (consequence 2), and the system being destroyed (consequence 3). The probability of occurrence of each path is the product of the given event probabilities because they all must occur for the given outcome to occur. The total for each outcome is then the summation of all the probabilities leading to that outcome.
For example, the probabilities of the top two branches of an event tree are:
P (P n)= R1 * R2 * .... * Rn
P (P n - 1) = R1 * R2 * .... * Rn- 1 * Q
Where:
P (P n) =The probability of occurrence of path n.
R= The reliability of the event.
Q= The unreliability of the event